一类跳跃扩散型股价过程组欧式未定权益定价

The Valuation of European Contingent Claims about Several StocksWhose Prices Are Governed by Brownian Motions and Poisson Processes

本文仅讨论一种类型的证券市场模型,其d种股票的价格过程满足一特殊的跳跃扩散型随机微分方程组,即市场风险源的个数与市场风险证券的个数相同．文章给出了这一模型下相应的跳跃扩散型倒向随机微分方程组适应解的存在唯一性定理及联系于跳跃扩散型多股票价格过程欧式未定权益(简记ECC)定价的基本公式,最后在常系数条件下导出了一种特殊形式欧式未定权益定价的Black-Scholes公式．

A model of security market in which the prices of d stocks are governed by a m-dimensional Brownian motionand a l-dimentional Poisson process (d = m +l ) is considered. The existence and umqueness of the adaptedsolutions with respect to the jump-diffusion backward stochastic differential equations for this market model are proved . It is then applied to obtain the fundamental valuation formula of European contingent claims about several stocks. Finally, under the conditions where the model coefficients are all constant, the Black-Scholespricing formulas for a special class of European coutingent claim is obtained .